John Nelder
Encyclopedia
John Ashworth Nelder FRS (8 October 1924 – 7 August 2010) was a British statistician
known for his contributions to experimental design
, analysis of variance
, computational statistics
, and statistical theory
.
, Nelder developed and supervised the updating of the statistical software packages GLIM
and GenStat
: Both packages are flexible high-level programming language
s that allow statisticians to formulate linear models concisely. GLIM influenced later environments for statistical computing
such as S-PLUS
and R
. Both GLIM and GenStat have powerful facilities for the analysis of variance
for block
experiments
, an area where Nelder has made many contributions.
In statistical theory
, Nelder and Wedderburn proposed the generalized linear model
. Generalized linear models were formulated by John Nelder and Robert Wedderburn
as a way of unifying various other statistical models, including linear regression
, logistic regression
and Poisson regression
. They proposed an iteratively reweighted least squares method
for maximum likelihood
estimation of the model parameters.
In statistical inference
, Nelder (along with George Barnard
and A. W. F. Edwards
) has emphasized the importance of the likelihood
in data analysis
, promoting this "likelihood approach" as an alternative to frequentist and Bayesian
statistics.
In response-surface
optimization
, Nelder and Roger Mead proposed the Nelder-Mead simplex heuristic, which is often used in engineering and statistics.
, near Dulverton
, Somerset
, Nelder was educated at Blundell's School
and Sidney Sussex College
, Cambridge, where he read mathematics.
Nelder's appointments included Head of the Statistics Section at the National Vegetable Research Station
, Wellesbourne
from 1951 to 1968 and Head of the Statistics Department at Rothamsted Experimental Station
from 1968 to 1984. During his time at Wellesbourne he spent a year(1965–1966) at the Waite Institute in Adelaide, South Australia, where he worked with Graham Wilkinson on Genstat. He held an appointment as Visiting Professor at Imperial College London
from 1972 onwards.
Nelder was elected a Fellow of the Royal Society in 1976 and received the Royal Statistical Society
's Guy Medal
in gold in 2005.
Nelder was responsible, with Max Nicholson and James Ferguson-Lees
, for debunking the Hastings Rarities
- a series of rare birds, preserved by a taxidermist
and provided with bogus histories.
Nelder died on 7 August 2010 in Luton and Dunstable Hospital, where he was recovering from a fall.
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
known for his contributions to experimental design
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
, analysis of variance
Analysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
, computational statistics
Computational statistics
Computational statistics, or statistical computing, is the interface between statistics and computer science. It is the area of computational science specific to the mathematical science of statistics....
, and statistical theory
Statistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
.
Contributions
Nelder's work was very influential in statistics. While leading research at Rothamsted Experimental StationRothamsted Experimental Station
The Rothamsted Experimental Station, one of the oldest agricultural research institutions in the world, is located at Harpenden in Hertfordshire, England. It is now known as Rothamsted Research...
, Nelder developed and supervised the updating of the statistical software packages GLIM
GLIM (software)
GLIM is a statistical software program for fitting generalized linear models .It was developed by the Royal Statistical Society'sWorking Party on Statistical Computing...
and GenStat
GenStat
GenStat is a general statistical package. Early versions were developed for large mainframe computers. Up until version 5, there was a Unix binary available, and this continues to be used by many universities and research institutions...
: Both packages are flexible high-level programming language
High-level programming language
A high-level programming language is a programming language with strong abstraction from the details of the computer. In comparison to low-level programming languages, it may use natural language elements, be easier to use, or be from the specification of the program, making the process of...
s that allow statisticians to formulate linear models concisely. GLIM influenced later environments for statistical computing
Computational statistics
Computational statistics, or statistical computing, is the interface between statistics and computer science. It is the area of computational science specific to the mathematical science of statistics....
such as S-PLUS
S-PLUS
S-PLUS is a commercial implementation of the S programming language sold by TIBCO Software Inc..It features object-oriented programming capabilities and advanced analytical algorithms.-Historical timeline:...
and R
R (programming language)
R is a programming language and software environment for statistical computing and graphics. The R language is widely used among statisticians for developing statistical software, and R is widely used for statistical software development and data analysis....
. Both GLIM and GenStat have powerful facilities for the analysis of variance
Analysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
for block
Randomized block design
In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to the experimenter...
experiments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
, an area where Nelder has made many contributions.
In statistical theory
Statistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
, Nelder and Wedderburn proposed the generalized linear model
Generalized linear model
In statistics, the generalized linear model is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to...
. Generalized linear models were formulated by John Nelder and Robert Wedderburn
Robert Wedderburn (statistician)
Robert William Maclagan Wedderburn was a Scottish statistician who worked at the Rothamsted Experimental Station. He was co-developer, with John Nelder, of the generalized linear model methodology,...
as a way of unifying various other statistical models, including linear regression
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
, logistic regression
Logistic regression
In statistics, logistic regression is used for prediction of the probability of occurrence of an event by fitting data to a logit function logistic curve. It is a generalized linear model used for binomial regression...
and Poisson regression
Poisson regression
In statistics, Poisson regression is a form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown...
. They proposed an iteratively reweighted least squares method
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method...
for maximum likelihood
Maximum likelihood
In statistics, maximum-likelihood estimation is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters....
estimation of the model parameters.
In statistical inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
, Nelder (along with George Barnard
George Alfred Barnard
George Alfred Barnard was a British statistician known particularly for his work on the foundations of statistics and on quality control.-Biography:...
and A. W. F. Edwards
A. W. F. Edwards
Anthony William Fairbank Edwards is a British statistician, geneticist, and evolutionary biologist, sometimes called Fisher's Edwards. He is a Life Fellow of Gonville and Caius College and retired Professor of Biometry at the University of Cambridge, and holds both the ScD and LittD degrees. A...
) has emphasized the importance of the likelihood
Likelihood function
In statistics, a likelihood function is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values...
in data analysis
Data analysis
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making...
, promoting this "likelihood approach" as an alternative to frequentist and Bayesian
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...
statistics.
In response-surface
Response surface methodology
In statistics, response surface methodology explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an...
optimization
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
, Nelder and Roger Mead proposed the Nelder-Mead simplex heuristic, which is often used in engineering and statistics.
Biography
Born in BrushfordBrushford, Somerset
Brushford is a village and civil parish south of Dulverton and north of Tiverton in Devon, in the West Somerset district of Somerset, England. According to the 2001 census it had a population of 535 in 243 households...
, near Dulverton
Dulverton
Dulverton is a town and civil parish in the heart of West Somerset, England, near the border with Devon. The town has a population of 1,630. The parish includes the hamlets of Battleton and Ashwick which is located approximately north west of Dulverton...
, Somerset
Somerset
The ceremonial and non-metropolitan county of Somerset in South West England borders Bristol and Gloucestershire to the north, Wiltshire to the east, Dorset to the south-east, and Devon to the south-west. It is partly bounded to the north and west by the Bristol Channel and the estuary of the...
, Nelder was educated at Blundell's School
Blundell's School
Blundell's School is a co-educational day and boarding independent school located in the town of Tiverton in the county of Devon, England. The school was founded in 1604 by the will of Peter Blundell, one of the richest men in England at the time, and relocated to its present location on the...
and Sidney Sussex College
Sidney Sussex College, Cambridge
Sidney Sussex College is a constituent college of the University of Cambridge in England.The college was founded in 1596 and named after its foundress, Frances Sidney, Countess of Sussex. It was from its inception an avowedly Puritan foundation: some good and godlie moniment for the mainteynance...
, Cambridge, where he read mathematics.
Nelder's appointments included Head of the Statistics Section at the National Vegetable Research Station
Horticulture Research International
Warwick HRI, formerly part of Horticulture Research International, is an United Kingdom organisation tasked with carrying out horticultural research and development and transferring the results to industry in England....
, Wellesbourne
Wellesbourne
Wellesbourne is a large village and civil parish in the county of Warwickshire, in the West Midlands region of the UK. In the 2001 census the parish, which also includes the village of Walton, had a population of 5,691 Wellesbourne is a large village and civil parish in the county of Warwickshire,...
from 1951 to 1968 and Head of the Statistics Department at Rothamsted Experimental Station
Rothamsted Experimental Station
The Rothamsted Experimental Station, one of the oldest agricultural research institutions in the world, is located at Harpenden in Hertfordshire, England. It is now known as Rothamsted Research...
from 1968 to 1984. During his time at Wellesbourne he spent a year(1965–1966) at the Waite Institute in Adelaide, South Australia, where he worked with Graham Wilkinson on Genstat. He held an appointment as Visiting Professor at Imperial College London
Imperial College London
Imperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
from 1972 onwards.
Nelder was elected a Fellow of the Royal Society in 1976 and received the Royal Statistical Society
Royal Statistical Society
The Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824...
's Guy Medal
Guy Medal
The Guy Medals are awarded by the Royal Statistical Society in three categories; Gold, Silver and Bronze. The Gold Medal is awarded triennially, the other two are awarded annually...
in gold in 2005.
Nelder was responsible, with Max Nicholson and James Ferguson-Lees
James Ferguson-Lees
I. James Ferguson-Lees is a British ornithologist. He spent his early years in Italy and France, but was educated in Bedford, England. He turned down the chance to study zoology at Oxford University in order to get married, and became a teacher for seven years...
, for debunking the Hastings Rarities
Hastings Rarities
The Hastings Rarities affair is a case of putative ornithological fraud. Two articles in the August 1962 issue of the journal British Birds, one a statistical examination by John Nelder, the other an editorial by Max Nicholson and James Ferguson-Lees, made a case for several records of birds...
- a series of rare birds, preserved by a taxidermist
Taxidermy
Taxidermy is the act of mounting or reproducing dead animals for display or for other sources of study. Taxidermy can be done on all vertebrate species of animals, including mammals, birds, fish, reptiles, and amphibians...
and provided with bogus histories.
Nelder died on 7 August 2010 in Luton and Dunstable Hospital, where he was recovering from a fall.
80th birthday tribute
- Methods and Models in Statistics: In Honour of Professor John Nelder, FRS edited by Niall Adams, Martin Crowder, David J Hand & Dave Stephens, Imperial College Press (2004). Imperial College Press Newsletter
Selected publications
- JN and R. W. M. Wedderburn, "Generalized Linear Models", J. R. Statist. Soc. A, 135 (1972) 370-384.
- McCullagh, P.Peter McCullaghPeter McCullagh is an Irish statistician, originally from Plumbridge, Northern Ireland. He attended Birmingham University and completed his Ph.D. at Imperial College London under Sir David Cox and Anthony Atkinson. He is currently the John D...
and J.A. Nelder. 1989. Generalized Linear Models. 2nd ed. Chapman & Hall/CRC, Boca Raton, Florida. ISBN 0-412-31760-5 - Lee, Y., J.A. Nelder, and Y. Pawitan. 2006. Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood. Chapman & Hall/CRC, Boca Raton, Florida. ISBN 1-58488-631-5